Question

I need help with 2b.

The topic is rational equations and restrictions are 2 and 0.

As my answer I got 0 = 8 but I’m unsure if that’s correct...

Answer 1

The answer to your question

a) Values excluded = -2, 0

b) solutions = -2/3, 2

Explanation:

Equation

`(4x)/(2x + 4) = (x+ 2)/(2x)`

a) x is restricted when the denominators equal zero, so let's get them.

2x + 4 = 0 2x = 0

2x = - 4 x = 0 / 2

x = -4 / 2 x = 0

x = -2

x must be different to -2, 0

b)
`(4x)/(2x + 4) = (x+ 2)/(2x)`

`(2x)/(x + 2) = (x + 2)/(2x)`

4x² = (x + 2)²

4x² = x² + 4x + 4

4x² - x² - 4x - 4 = 0

3x² - 4x - 4 = 0

3x² - 6x + 2x - 4 = 0

3x(x - 2) + 2(x - 2) = 0

(x - 2)(3x + 2) = 0

x₁ - 2 = 0 3x₂ + 2 = 0

x₁ = 2 x₂ = -2/3